Evidence versus Proof

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fast
 
Reply Mon 16 Nov, 2009 10:50 am
@Emil,
Sorry for the extended delay. I've been trying to single-handedly harness the mighty power of pure hate so that I can gleefully direct it towards any and all pain causing dentists.

[QUOTE=Emil;103445]When someone says that he is e-certain that he knows that the Earth is round. What do you say to him?

When someone says that he is e-certain that 1+1=2. What do you say to him?[/QUOTE]

When someone says that he or she is epistemically certain about something, and if he or she actually means what the term, "epistemically certain" means, then I'm going to conclude that the person is incorrect; thus, my conclusion is that he or she is not epistemically certain that he knows that the Earth is round or epistemically certain that 1+1=2. This isn't to say they are mistaken about what they know (i.e. that the Earth is round and that 1+1=2). The issue is no longer about whether they're mistaken about what they know. The issue morphs into whether or not it's impossible for them to be mistaken.
 
Zetherin
 
Reply Mon 16 Nov, 2009 10:50 am
@kennethamy,
kennethamy;103842 wrote:
Both. Unless he means, "feel certain".


Can one be e-certain about anything?
 
kennethamy
 
Reply Mon 16 Nov, 2009 10:56 am
@Zetherin,
Zetherin;103852 wrote:
Can one be e-certain about anything?


Very little, if anything. Maybe that I exist. But I certainly am not sure. But, if even about that, then, so what?
 
fast
 
Reply Mon 16 Nov, 2009 11:25 am
@fast,
Evidence doesn't have to establish the truth for which it is used to establish in order for what is used as evidence to be evidence. With proof, however, it's different.

If I provide my identification as evidence that I am who I say I am, then not only have I provided evidence that I am who I say I am, but I have also provided proof that I am who I say I am. But, this is a simple case.

If my brother provides my identification as evidence that he is who he says he is, then yes, he has provided evidence, and yes, he has provided evidence that he is who he says he is (believe it or not!), but although he has provided the evidence as proof that he is who he says he is, he didn't actually provide proof that he is who he said he is because my identification doesn't prove that he is me.

So, in the simple case, evidence serves as proof, but in the complex case, the evidence does not serve as proof. In both cases, evidence is provided, but only in the simple case was there actual proof.

What's interesting to me is that although we can have evidence for what doesn't exist, we can't have proof for what doesn't exist.
 
kennethamy
 
Reply Mon 16 Nov, 2009 11:34 am
@fast,
fast;103862 wrote:

What's interesting to me is that although we can have evidence for what doesn't exist, we can't have proof for what doesn't exist.


"To prove" is a "success verb" like, "to win". But "to present evidence for something" is a process verb like, "to race". You race in order to win, and you present evidence in order to prove. But you may race, and not win. And you may present evidence, an not prove.
 
Emil
 
Reply Mon 16 Nov, 2009 11:52 am
@kennethamy,
kennethamy;103842 wrote:
Both. Unless he means, "feel certain".


No no. I'm not talking about psychological certainty. That seems somewhat uninteresting in relation to this thread.
 
Zetherin
 
Reply Mon 16 Nov, 2009 11:58 am
@kennethamy,
kennethamy;103853 wrote:
Very little, if anything. Maybe that I exist. But I certainly am not sure. But, if even about that, then, so what?


If noone is e-certain of anything, because everyone is fallible, what does using the term "e-certain" allow us then, epistemologically or philosophically? What does it clarify, or help explain, in logic?

To say that someone isn't e-certain about something when what we mean is that that someone is fallible, seems all too pointless; it's common sense that that someone is fallible.
 
Emil
 
Reply Mon 16 Nov, 2009 11:58 am
@fast,
fast;103851 wrote:
Sorry for the extended delay. I've been trying to single-handedly harness the mighty power of pure hate so that I can gleefully direct it towards any and all pain causing dentists.



When someone says that he or she is epistemically certain about something, and if he or she actually means what the term, "epistemically certain" means, then I'm going to conclude that the person is incorrect; thus, my conclusion is that he or she is not epistemically certain that he knows that the Earth is round or epistemically certain that 1+1=2. This isn't to say they are mistaken about what they know (i.e. that the Earth is round and that 1+1=2). The issue is no longer about whether they're mistaken about what they know. The issue morphs into whether or not it's impossible for them to be mistaken.
 
Zetherin
 
Reply Mon 16 Nov, 2009 12:07 pm
@fast,
Emil wrote:
And if I am wrong, then it is possible to believe that one exists and yet not exist. Or what?


One cannot believe a contradiction, as far as I know.
 
Emil
 
Reply Mon 16 Nov, 2009 12:12 pm
@fast,
fast;103862 wrote:
Evidence doesn't have to establish the truth for which it is used to establish in order for what is used as evidence to be evidence. With proof, however, it's different.


You seem to say that evidence not need increase the probability of the conclusion to 1 ("establishing the truth") but proof does. Maybe. But I disthink so. I use "proof" more broadly than that and most people do like me. A proof is merely very strong evidence.

The limited notion of "proof" that you seem to be talking about is the proof of mathematics and logic.

Isn't that so?

fast;103862 wrote:
If I provide my identification as evidence that I am who I say I am, then not only have I provided evidence that I am who I say I am, but I have also provided proof that I am who I say I am. But, this is a simple case.


I don't know what identification you provided, so I will not say that you did provide proof. However in the limited sense of "proof", you did not provide proof since the evidence did not increase the probability of the conclusion to 1. No identification that I know of could ever be proof in the limited sense.

fast;103862 wrote:
If my brother provides my identification as evidence that he is who he says he is, then yes, he has provided evidence, and yes, he has provided evidence that he is who he says he is (believe it or not!), but although he has provided the evidence as proof that he is who he says he is, he didn't actually provide proof that he is who he said he is because my identification doesn't prove that he is me.

So, in the simple case, evidence serves as proof, but in the complex case, the evidence does not serve as proof. In both cases, evidence is provided, but only in the simple case was there actual proof.


Depending on the identification used, it may or may not provide proof for your brother. But it did not provide proof in the limited sense.

fast;103862 wrote:
What's interesting to me is that although we can have evidence for what doesn't exist, we can't have proof for what doesn't exist.


So you say. Is this the "You can't prove a negative."? I might disagree depending on what is meant by that.

-

To recap. There are (at least) two sense of "proof".

  • The general sense where "proof" means (very) strong evidence. In symbols(ish). Pr(p|proof)>>Pr(p|evidence). We may refer to this as g-proof for general proof.
  • The limited sense used in mathematics and logic where proof is what "establishes the truth of the conclusion". Formally Pr(p|proof)=1. We may refer to this as l-proof for limited proof.

Alternatively we could stipulate in this context only to use proof in the limited sense (l-proof). Another alternative is that we could refer to them as weak and strong proof or with adverbs weakly proves and strongly proves.

---------- Post added 11-16-2009 at 07:14 PM ----------

Zetherin;103872 wrote:
One cannot believe a contradiction, as far as I know.


You may want to learn about paraconsistent logic (SEP, Wiki
 
Zetherin
 
Reply Mon 16 Nov, 2009 12:31 pm
@fast,
Emil wrote:

They still believe in things that imply a contradiction.


Can you give me an example?
 
fast
 
Reply Mon 16 Nov, 2009 12:38 pm
@Emil,
[QUOTE=Emil;103871]But this understanding of epistemic certainty seems uninteresting to me. There are other understandings. [/QUOTE]The term refers to what it does and nothing else.



I'm afraid I don't quite get that.

[QUOTE]Are there anything that are we EC2 about? Maybe. [/QUOTE]I think that we are perhaps epistemically certain about only a few things, but now that you add a second denotation, I'm no longer certain (that is, confident) that we're necessarily talking about the same thing.

The issue of epistemic certainty is hard enough to pin down without the suggestion that various understandings of epistemic certainty somehow alter what it is.

We do not have to be immune to error or mistake to know what we think we do. I can know what I know and it be possible that I could have been mistaken, but so long as I'm not actually mistaken, then so what! That I could have been wrong doesn't imply that I am, and not being wrong is what's important-not the possibility that I could have been.

[QUOTE]Is it possible to believe that one exists, and one does not exist? [/QUOTE]That's ambiguous. I think it's possible to be in both South Carolina and Florida. Don't you?
 
Zetherin
 
Reply Mon 16 Nov, 2009 12:44 pm
@fast,
fast wrote:
That's ambiguous.
Quote:
I think it's possible to be in both South Carolina and Florida. Don't you?


But how is that a contradiction (for instance, someone could call the same place two different names)? Wouldn't the contradiction be, is it possible to be in South Carolina and not in South Carolina at the same time, or possible to be in Florida and not in Florida at the same time? No one would believe that they're in X and not in X at the same time, as far as I know.
 
kennethamy
 
Reply Mon 16 Nov, 2009 12:47 pm
@Zetherin,
Zetherin;103870 wrote:
If noone is e-certain of anything, because everyone is fallible, what does using the term "e-certain" allow us then, epistemologically or philosophically? What does it clarify, or help explain, in logic?

To say that someone isn't e-certain about something when what we mean is that that someone is fallible, seems all too pointless; it's common sense that that someone is fallible.


I am always happy to agree with commonsense. What is wrong with that? It is a good thing to recognize that we are all fallible. Otherwise we become dogmatists, or, on the other extreme, skeptics. Fallibilism is the happy medium. Not too hot, and not too cold, but, as Goldilocks said, "just right!".
 
Zetherin
 
Reply Mon 16 Nov, 2009 12:50 pm
@kennethamy,
kennethamy;103881 wrote:
I am always happy to agree with commonsense. What is wrong with that? It is a good thing to recognize that we are all fallible. Otherwise we become dogmatists, or, on the other extreme, skeptics. Fallibilism is the happy medium. Not too hot, and not too cold, but, as Goldilocks said, "just right!".


I also agree that we are fallible. I just don't agree we need some fancy term like "epistemically certain" to remind us of such. Unless a new term clarifies, instead of confuses, it is useless. In other words, I see no reason to use "e-certain". I'll stick with my commonsense, without showy, intellectual rapages.
 
Emil
 
Reply Mon 16 Nov, 2009 12:54 pm
@Zetherin,
Zetherin;103870 wrote:
If noone is e-certain of anything, because everyone is fallible, what does using the term "e-certain" allow us then, epistemologically or philosophically? What does it clarify, or help explain, in logic?

To say that someone isn't e-certain about something when what we mean is that that someone is fallible, seems all too pointless; it's common sense that that someone is fallible.


Some people seem to think that we are indeed e-certain about certain things. Like knowledge. Or that we exist. Or our mental states. This has some implications.

---------- Post added 11-16-2009 at 07:56 PM ----------

Zetherin;103876 wrote:
Can you give me an example?


I did before. Paraconsistent logics. They allow for contradictions. Priest, a notable proponent of paraconsistent logics, even believes in contradictions about a couple of things like change and semantics paradoxes ("This sentence is false").
 
kennethamy
 
Reply Mon 16 Nov, 2009 01:00 pm
@Zetherin,
Zetherin;103882 wrote:
I also agree that we are fallible. I just don't agree we need some fancy term like "epistemically certain" to remind us of such. Unless a new term clarifies, instead of confuses, it is useless. In other words, I see no reason to use "e-certain".


I think the point of using "e-certain" is to distinguish between psychological or subjective certainty, and objective certainty. The former refers to one's feeling or conviction that some belief one holds is true. It does not imply truth, since one can be convinced that what one believes is true, and be mistaken. The latter refers not to feeling or conviction of truth, but to the impossibility of mistake. If my belief must be true, then I am e-certain. The question is whether I am e-certain about any proposition I believe is true. Some people, for instance, think that I cannot be mistaken if I believe that I am in pain; or that I exist.
 
Zetherin
 
Reply Mon 16 Nov, 2009 01:02 pm
@fast,
Emil wrote:

Some people seem to think that we are indeed e-certain about certain things.


Here, did you mean "certain" as in certain (to be sure - ie. I'm certain he will come to the party), or certain (specificity - ie. I picked a certain dress to wear this evening)? I think you meant the latter, but I just wanted to make sure.

Quote:
Like knowledge. Or that we exist. Or our mental states. This has some implications.


I often times don't know that I know something. I often doubt myself, but then find out later that I knew all along. I often times don't know how I feel, or what mental state I'm in. And, even after intense introspection, I'm still not e-certain about my feelings.

I don't think I can trust my sanity enough to claim that I'm e-certain (using it as we've addressed it) about anything. But, I suppose others can...
 
Emil
 
Reply Mon 16 Nov, 2009 01:04 pm
@fast,
[QUOTE=fast;103877]The term refers to what it does and nothing else.[/QUOTE]

"Refer" is usually used about particulars like "this dog". They refer to something, an object in this case a specific dog. Many words (all?) and phrases are ambiguous, that is, they mean something at one time and another thing at another time.

[QUOTE=fast;103877]
I'm afraid I don't quite get that.[/QUOTE]

Perhaps because I was a little too quick. I wrote "someone", but it should be "something". (As in "believe something".)

[QUOTE=fast;103877]
I think that we are perhaps epistemically certain about only a few things, but now that you add a second denotation, I'm no longer certain (that is, confident) that we're necessarily talking about the same thing.[/QUOTE]

Ok. What epistemic certainty are you talking about? Can you offer a definition? Some paradigm examples of its use? The notion seems vague to me.

[QUOTE=fast;103877]
The issue of epistemic certainty is hard enough to pin down without the suggestion that various understandings of epistemic certainty somehow alter what it is.[/QUOTE]

Which I why I try to clarify the individual meanings of it, if there are multiple. I think there are. The phrase is relatively vague or ambiguous. If there are not, it still needs clarification.

[QUOTE=fast;103877]
We do not have to be immune to error or mistake to know what we think we do. I can know what I know and it be possible that I could have been mistaken, but so long as I'm not actually mistaken, then so what! That I could have been wrong doesn't imply that I am, and not being wrong is what's important-not the possibility that I could have been.[/QUOTE]

Ok.

[QUOTE=fast;103877]
That's ambiguous. I think it's possible to be in both South Carolina and Florida. Don't you?[/QUOTE]

Yes it is. But I typed it anyway because the symbols above clarify what I mean. You could change it to this though:
[INDENT] Is it possible (to believe that one exists, and one does not exist)? [/INDENT]

---------- Post added 11-16-2009 at 08:06 PM ----------

Zetherin;103880 wrote:
 
Zetherin
 
Reply Mon 16 Nov, 2009 01:09 pm
@fast,
Emil wrote:

What is ambigious about the contradiction, X exists and X does not exist? I suppose the answer lies in paraconsistent logic?
 
 

 
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